We present light-cone-integrated simulations of the cosmic microwave background (CMB) polarization signal induced by a single scattering in the direction of clusters of galaxies and filaments. We characterize the statistical properties of the induced polarization signals from the presence of the CMB quadrupole component (pqiCMB) and as the result of the transverse motion of ionized gas clouds with respect to the CMB rest frame (pbeta super(2)lSZ). Our simulation method involves a box-stacking scheme that allows to reconstruct the CMB quadrupole component and the gas physical properties along the line of sight. We find that the linear polarization degree in the logarithmic scale of both effects follows approximately a Gaussian distribution and the mean total signal is about 10 super(-8) and 10 super(-10) for the pqiCMB and pbeta super(2)lSZ effects, respectively. Our results suggest that most of the contribution for the total polarization signal arises from z lap 4 for the pqiCMB and z lap 3 for pbeta super(2)lSZ.